After you have fed your sourdough starter, save the discard in a separate bowl. You should have about a cup. If you have a little more or less, that's fine. You can make up the difference with buttermilk.
In a large bowl, cream the butter and the sugar together on medium-high speed until light and fluffy. About 2 minutes using a hand mixer, or longer if you're using a whisk.
While mixing on low, add in the eggs one at a time and mix on medium speed until combined. (Remember to make sure they are room temp or even a little warm or they won't mix in properly.)
While mixing on low, add in the sourdough discard, buttermilk, baking powder, baking soda, salt, vanilla, and nutmeg. Mix until just combined.
Sprinkle in the flour and combine on low until the dough comes together. It will be sticky.
Cutting and frying the donuts
Place the dough onto a lightly floured surface. Press it down with your hand to about 1″ tall. Fold the dough over onto itself 3-4 times until it looks a bit smoother but don’t overwork it or the dough will get tough.
Press the dough down to about ½″ thick and dust with a bit of flour. Let it rest for 5-10 minutes. Now is the perfect time to start heating up your oil. Use a large heavy pot like a dutch oven and 2" of oil. (About 4 cups.) Heat on medium heat until the temperature reaches 360º-375ºF. This should take about 15 minutes.
Use a donut cutter or metal ring cutter to cut out the donuts. (Don't forget to cut out the centers.) Try to leave as little space as possible between the donuts. Set the holes aside to fry at the end. Press the leftover scraps together and continue cutting donuts. You should get 10-12 donuts with a 4″ cutter. More if you’re using a smaller cutter.
Use a slotted spatula or skimmer to lower the donut into the hot oil. The doughnut will start bubbling a ton at first then settle down as a crispy outer layer develops. Fry for 2 minutes, flip the donut and fry for 1 more minute.
Remove the donut from the oil with the slotted spoon and transfer to a cooling rack over a sheet pan. Fry your donut holes at the end for about 1 minute, stirring and pushing them down with your spoon until golden brown. Let your donuts cool before using.
The glaze
In a medium bowl, combine 1 cup sifted powdered sugar with 2 Tablespoons of water (or milk) and whisk until smooth. Add more water for a thinner glaze, or more powdered sugar for a thicker glaze. Grasp the sides of each donut and dunk the top into the glaze, or drizzle on the glaze.
Store your donuts in a plastic or paper bag at room temperature for about 3 days, the crispy outer layer will soften over time.
If you don't have any buttermilk on hand, you can make your own buttermilk substitute.
Make sure your eggs, buttermilk, and butter are all room temperature so that the ingredients combine together well. If your eggs or milk are too cold, they will not mix with the butter and your donuts won’t rise properly.
Bring the oil to a temperature between 360ºF-375ºF (182ºC-190ºC). You can save yourself a lot of headaches by using a candy thermometer or infrared heat thermometer to measure the temperature of your oil.
I use a FryDaddy to fry my donuts because it regulates the temperature while frying, but you can also use a deep heavy pot with high sides. Make sure to test the temperature of the oil frequently.
Don't add too many donuts to the oil. It causes the heat of the oil to drop drastically and could make your donuts oily. Fry 2 or 3 donuts at a time depending on the size of your pot.
The best oil to use for deep frying is one that has a high smoke point and a neutral flavor. In my research I found the best oils to use are peanut oil, vegetable oil, canola oil, vegetable shortening, or lard. I prefer to use Lard because it is dairy-free, creates a very crisp outer layer on the donuts, and is minimally processed.